13789 ÷ 7 = 1969 R6
Alright, let's work through the division of 13789 by 7 step by step.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 2:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 13 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 7

Step 3:
7 goes into 67 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 63 from 67 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 7

Step 4:
7 goes into 48 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 196
Subtract 42 from 48 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 7

Step 5:
7 goes into 69 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 1969
Subtract 63 from 69 to get 6.

The final result is 1969 with a remainder of 6.